Really hard Chem test prep problem. Help please?

Question

A sample of gaseous neon atoms at atmospheric pressure and 0 contains atoms per liter. The atomic radius of neon is 69 . What fraction of the space is occupied by the atoms themselves? Thanks everyone

The 0 is suppose to be 0 degrees celcius and the 69 is pico meters (pm).Thanks

Answer 1

Using an ideal gas formula:
PV = nRT
Considering one mole of gas, you get: P/RT = 1/V
or 1/(0.0820578* 273.15) = 0.044615 = 1/V, thus V = 22.4 (L)
Now, one mole contains 6.022x10^23 atoms. Assume each atom is of spherical shape, these atoms have a volume of:
6.022x10^23 * (4/3)pi*(69x10^(-11))^3 = 0.0008287 (L)
Thus the final answer is:
0.0008287L / 22.4L = 3.70x10^(-5)
which is such a small fraction of the gas volume.